Two particles travel along the space curves r1(t) = (t^3 , t^2 , t), r2(t) = (1 + 2t, 1 + 3t, 1 + 4t). Each of these curves gives the position vector for the particle at a given time t. (a) Do the particles collide? (b) Do their paths intersect? (c) For each curve, at the point corresponding to t = 2 find the tangent line the curve